An integrated heat pump and water heating circuit for space heating and cooling and heating domestic water. The circuit includes a first heat exchanger for the domestic water, a second heat exchanger for the source, a third exchanger for the space, and a variable capacity compressor. The circuit has four modes of operation. In the first mode, the space is cooled. In the second mode, the space is heated. In the third mode, the circuit heats the water supply. In a fourth mode, the water supply is heated and the space is cooled simultaneously. The speed of the compressor is adjusted to maintain a pressure differential at or above a predetermined set point.